Question: Simplify the following expression: $k = \dfrac{20bc - 20c^2}{20bc + 5ac} - \dfrac{20c^2}{20bc + 5ac}$ You can assume $a,b,c \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{20bc - 20c^2 - (20c^2)}{20bc + 5ac}$ $k = \dfrac{20bc - 40c^2}{20bc + 5ac}$ The numerator and denominator have a common factor of $5c$, so we can simplify $k = \dfrac{4b - 8c}{4b + a}$